She shivered from the cold.

Literal

She [topic-は] coldness [from-に] shivered.

寒さ is the noun form of the i-adjective 寒い ('cold'), built with the productive ~さ suffix that turns adjectives into nouns expressing the quality measured (高さ 'height,' 大きさ 'size'). に here marks the cause/trigger of the shivering — a slightly literary use of に that pairs with involuntary physical reactions (恐怖に震える 'shiver in fear,' 喜びに泣く 'cry from joy'). The single-clause shape and past-tense 震えた frame this as a discrete past event, not an ongoing state — a single shudder rather than continuous shivering. The alternative particle で would be more neutral and everyday, lighter on the literary feel than this に.